On the complexity of the maximum common subgraph problem for partial k-trees of bounded degree

Abstract

This paper considers two versions of the maximum common subgraph problem for vertex-labeled graphs: the maximum common connected edge subgraph problem and the maximum common connected induced subgraph problem. The former is to find a connected graph with the maximum number of edges that is isomorphic to a subgraph of each of the two input graphs. The latter is to find a common connected induced subgraph with the maximum number of vertices. This paper shows that both problems are NP-hard even for labeled partial k-trees of bounded degree. It also presents some exponential-time algorithms for both problems. © Springer-Verlag 2012.